# Example 958 — Half the voltage was a quarter of the heat `half_the_voltage_was_a_quarter_of_the_heat.eml` - A 2000-watt heater built for a 240-volt country is plugged into a 120-volt supply with a plug adapter, the traveller reasons that half the voltage means half the heat and a slow but working heater, and the room barely warms. What half the voltage does to a fixed resistance is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A 2000-watt # heater built for a 240-volt country is plugged into a 120-volt supply with a # plug adapter, the traveller reasons that half the voltage means half the # heat and a slow but working heater, and the room barely warms. What half the # voltage does to a fixed resistance is computed below. # # The reasoning is careful. The voltages are right; the heater is a plain # resistive element, exactly the kind that tolerates a lower voltage; half the # voltage genuinely is half the current; and the intent was exactly 'half the # heat, twice the time'. # # Power in a resistor is voltage times current, and halving the voltage halves # the current too, so the power falls to a quarter - 500 watts, not 1000 - and # the transformer that would restore it draws twice the current from the # 120-volt side, past what a 15-amp circuit allows. 240 => rated_volts 2000 => rated_watts 120 => supply_volts 150 => circuit_breaker_tenths_of_an_amp int(rated_volts * rated_volts * 10 / rated_watts) => element_resistance_tenths_of_an_ohm int(rated_watts * supply_volts * supply_volts / (rated_volts * rated_volts)) => watts_at_half_voltage int(rated_watts / 2) => watts_the_traveller_expected int(watts_at_half_voltage * 10000 / rated_watts) => power_as_a_share_of_rated_per_myriad int(rated_watts * 10 / rated_volts) => rated_current_tenths_of_an_amp int(watts_at_half_voltage * 10 / supply_volts) => current_at_half_voltage_tenths_of_an_amp int(rated_watts / watts_at_half_voltage) => times_longer_to_deliver_the_same_heat int(rated_watts * 10 / supply_volts) => transformer_input_current_tenths_of_an_amp transformer_input_current_tenths_of_an_amp - circuit_breaker_tenths_of_an_amp => transformer_current_over_the_breaker_tenths "heater : " + str(rated_watts) + " W at " + str(rated_volts) + " V, element " + str(element_resistance_tenths_of_an_ohm) + " tenths of an ohm" ^0 "supply : " + str(supply_volts) + " V, half" ^0 "" ^0 "current at " + str(rated_volts) + " V : " + str(rated_current_tenths_of_an_amp) + " tenths of an amp" ^0 "current at " + str(supply_volts) + " V : " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths of an amp, half" ^0 "power at " + str(supply_volts) + " V : " + str(watts_at_half_voltage) + " W, " + str(power_as_a_share_of_rated_per_myriad) + " per ten thousand of rated" ^0 "power the traveller expected : " + str(watts_the_traveller_expected) + " W" ^0 "time for the same heat : " + str(times_longer_to_deliver_the_same_heat) + " times as long, not twice" ^0 "" ^0 "a step-up transformer instead : full " + str(rated_watts) + " W, drawn from the " + str(supply_volts) + " V side at " + str(transformer_input_current_tenths_of_an_amp) + " tenths of an amp" ^0 "circuit breaker : " + str(circuit_breaker_tenths_of_an_amp) + " tenths of an amp, exceeded by " + str(transformer_current_over_the_breaker_tenths) ^0 "" ^0 # ---- what the traveller verified ---- "the half-and-half reasoning" ^0 " voltages : " + str(rated_volts) + " and " + str(supply_volts) + ", right" ^0 " element : plain resistance, tolerant of low voltage" ^0 " current : half the voltage, half the current" ^0 " intent : half the heat, twice the time" ^0 " facts wrong : 0" ^0 " verdict : HALF THE VOLTAGE IS HALF THE HEAT" ^0 "" ^0 " knowing that a resistive element takes half the current at" ^0 " half the voltage is the part done right here, and it is why" ^0 " " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths of an amp is exactly right" ^0 "" ^0 # ---- what half the voltage does to a resistor ---- "power is voltage times current" ^0 " at " + str(rated_volts) + " V : " + str(rated_volts) + " times " + str(rated_current_tenths_of_an_amp) + " tenths, " + str(rated_watts) + " W" ^0 " at " + str(supply_volts) + " V : the voltage halves AND the current halves," ^0 " " + str(supply_volts) + " times " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths, " + str(watts_at_half_voltage) + " W" ^0 " what halved once in the reasoning : one factor" ^0 " what halves in the element : both factors, a quarter" ^0 " what a transformer does : restores the voltage by doubling" ^0 " the current it pulls, " + str(transformer_input_current_tenths_of_an_amp) + " tenths from a " + str(circuit_breaker_tenths_of_an_amp) + "-tenth circuit" ^0 "" ^0 # ---- what the traveller got ---- "the room" ^0 " believed : " + str(watts_the_traveller_expected) + " W, warm in twice the time" ^0 " actual : " + str(watts_at_half_voltage) + " W, warm in " + str(times_longer_to_deliver_the_same_heat) + " times the time" ^0 " is the element damaged : no; it runs cool and happy" ^0 " is half the voltage half the heat : no; it is a quarter, and" ^0 " the transformer that fixes it trips the breaker" ^0 "" ^0 # ---- null control ---- # The same heater with its power computed from the voltage squared instead of # from the voltage alone. 1000 => nc_power_read_as_half_of_rated_watts 500 => nc_power_read_as_voltage_squared_watts 500 => nc_watts_the_second_halving_removes "null control - square the voltage" ^0 " power, read as half of rated : " + str(nc_power_read_as_half_of_rated_watts) + " W" ^0 " power, read from voltage squared : " + str(nc_power_read_as_voltage_squared_watts) + " W" ^0 " watts the second halving removes : " + str(nc_watts_the_second_halving_removes) ^0 " no heater and no supply changed; the current was allowed" ^0 " to fall along with the voltage it depends on" ^0 "" ^0 # ---- the rule ---- "what a resistive heater on half its voltage guarantees" ^0 " it draws half the current : exactly, " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths of an amp" ^0 " it gives half the heat : not addressed; heat is voltage times" ^0 " current and both halved, so " + str(watts_at_half_voltage) + " W, a quarter, and the" ^0 " transformer that restores " + str(rated_watts) + " W pulls " + str(transformer_input_current_tenths_of_an_amp) + " tenths through a" ^0 " " + str(circuit_breaker_tenths_of_an_amp) + "-tenth breaker" ^0 "" ^0 "halve one thing that is really a product of two and you have halved it" ^0 "twice; the voltage you can read on the wall, the current you cannot, and" ^0 "the heat is the pair of them" ^0 "" ^0 "Half the voltage is half the current - that step is right. But the heat is" ^0 "their product, so " + str(supply_volts) + " V into a " + str(rated_watts) + "-W element is " + str(watts_at_half_voltage) + " W, a quarter, taking " + str(times_longer_to_deliver_the_same_heat) ^0 "times as long, and the transformer that gives the full " + str(rated_watts) + " back draws " + str(transformer_input_current_tenths_of_an_amp) + " tenths" ^0 "of an amp past a " + str(circuit_breaker_tenths_of_an_amp) + "-tenth breaker, until the heat is read as the product it is." ^0 ``` ## Python (deterministic transpilation) ```python rated_volts = 240 rated_watts = 2000 supply_volts = 120 circuit_breaker_tenths_of_an_amp = 150 element_resistance_tenths_of_an_ohm = int(rated_volts * rated_volts * 10 / rated_watts) watts_at_half_voltage = int(rated_watts * supply_volts * supply_volts / (rated_volts * rated_volts)) watts_the_traveller_expected = int(rated_watts / 2) power_as_a_share_of_rated_per_myriad = int(watts_at_half_voltage * 10000 / rated_watts) rated_current_tenths_of_an_amp = int(rated_watts * 10 / rated_volts) current_at_half_voltage_tenths_of_an_amp = int(watts_at_half_voltage * 10 / supply_volts) times_longer_to_deliver_the_same_heat = int(rated_watts / watts_at_half_voltage) transformer_input_current_tenths_of_an_amp = int(rated_watts * 10 / supply_volts) transformer_current_over_the_breaker_tenths = transformer_input_current_tenths_of_an_amp - circuit_breaker_tenths_of_an_amp print("heater : " + str(rated_watts) + " W at " + str(rated_volts) + " V, element " + str(element_resistance_tenths_of_an_ohm) + " tenths of an ohm") print("supply : " + str(supply_volts) + " V, half") print("") print("current at " + str(rated_volts) + " V : " + str(rated_current_tenths_of_an_amp) + " tenths of an amp") print("current at " + str(supply_volts) + " V : " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths of an amp, half") print("power at " + str(supply_volts) + " V : " + str(watts_at_half_voltage) + " W, " + str(power_as_a_share_of_rated_per_myriad) + " per ten thousand of rated") print("power the traveller expected : " + str(watts_the_traveller_expected) + " W") print("time for the same heat : " + str(times_longer_to_deliver_the_same_heat) + " times as long, not twice") print("") print("a step-up transformer instead : full " + str(rated_watts) + " W, drawn from the " + str(supply_volts) + " V side at " + str(transformer_input_current_tenths_of_an_amp) + " tenths of an amp") print("circuit breaker : " + str(circuit_breaker_tenths_of_an_amp) + " tenths of an amp, exceeded by " + str(transformer_current_over_the_breaker_tenths)) print("") print("the half-and-half reasoning") print(" voltages : " + str(rated_volts) + " and " + str(supply_volts) + ", right") print(" element : plain resistance, tolerant of low voltage") print(" current : half the voltage, half the current") print(" intent : half the heat, twice the time") print(" facts wrong : 0") print(" verdict : HALF THE VOLTAGE IS HALF THE HEAT") print("") print(" knowing that a resistive element takes half the current at") print(" half the voltage is the part done right here, and it is why") print(" " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths of an amp is exactly right") print("") print("power is voltage times current") print(" at " + str(rated_volts) + " V : " + str(rated_volts) + " times " + str(rated_current_tenths_of_an_amp) + " tenths, " + str(rated_watts) + " W") print(" at " + str(supply_volts) + " V : the voltage halves AND the current halves,") print(" " + str(supply_volts) + " times " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths, " + str(watts_at_half_voltage) + " W") print(" what halved once in the reasoning : one factor") print(" what halves in the element : both factors, a quarter") print(" what a transformer does : restores the voltage by doubling") print(" the current it pulls, " + str(transformer_input_current_tenths_of_an_amp) + " tenths from a " + str(circuit_breaker_tenths_of_an_amp) + "-tenth circuit") print("") print("the room") print(" believed : " + str(watts_the_traveller_expected) + " W, warm in twice the time") print(" actual : " + str(watts_at_half_voltage) + " W, warm in " + str(times_longer_to_deliver_the_same_heat) + " times the time") print(" is the element damaged : no; it runs cool and happy") print(" is half the voltage half the heat : no; it is a quarter, and") print(" the transformer that fixes it trips the breaker") print("") nc_power_read_as_half_of_rated_watts = 1000 nc_power_read_as_voltage_squared_watts = 500 nc_watts_the_second_halving_removes = 500 print("null control - square the voltage") print(" power, read as half of rated : " + str(nc_power_read_as_half_of_rated_watts) + " W") print(" power, read from voltage squared : " + str(nc_power_read_as_voltage_squared_watts) + " W") print(" watts the second halving removes : " + str(nc_watts_the_second_halving_removes)) print(" no heater and no supply changed; the current was allowed") print(" to fall along with the voltage it depends on") print("") print("what a resistive heater on half its voltage guarantees") print(" it draws half the current : exactly, " + str(current_at_half_voltage_tenths_of_an_amp) + " tenths of an amp") print(" it gives half the heat : not addressed; heat is voltage times") print(" current and both halved, so " + str(watts_at_half_voltage) + " W, a quarter, and the") print(" transformer that restores " + str(rated_watts) + " W pulls " + str(transformer_input_current_tenths_of_an_amp) + " tenths through a") print(" " + str(circuit_breaker_tenths_of_an_amp) + "-tenth breaker") print("") print("halve one thing that is really a product of two and you have halved it") print("twice; the voltage you can read on the wall, the current you cannot, and") print("the heat is the pair of them") print("") print("Half the voltage is half the current - that step is right. But the heat is") print("their product, so " + str(supply_volts) + " V into a " + str(rated_watts) + "-W element is " + str(watts_at_half_voltage) + " W, a quarter, taking " + str(times_longer_to_deliver_the_same_heat)) print("times as long, and the transformer that gives the full " + str(rated_watts) + " back draws " + str(transformer_input_current_tenths_of_an_amp) + " tenths") print("of an amp past a " + str(circuit_breaker_tenths_of_an_amp) + "-tenth breaker, until the heat is read as the product it is.") ``` ## stdout (executed) ```text heater : 2000 W at 240 V, element 288 tenths of an ohm supply : 120 V, half current at 240 V : 83 tenths of an amp current at 120 V : 41 tenths of an amp, half power at 120 V : 500 W, 2500 per ten thousand of rated power the traveller expected : 1000 W time for the same heat : 4 times as long, not twice a step-up transformer instead : full 2000 W, drawn from the 120 V side at 166 tenths of an amp circuit breaker : 150 tenths of an amp, exceeded by 16 the half-and-half reasoning voltages : 240 and 120, right element : plain resistance, tolerant of low voltage current : half the voltage, half the current intent : half the heat, twice the time facts wrong : 0 verdict : HALF THE VOLTAGE IS HALF THE HEAT knowing that a resistive element takes half the current at half the voltage is the part done right here, and it is why 41 tenths of an amp is exactly right power is voltage times current at 240 V : 240 times 83 tenths, 2000 W at 120 V : the voltage halves AND the current halves, 120 times 41 tenths, 500 W what halved once in the reasoning : one factor what halves in the element : both factors, a quarter what a transformer does : restores the voltage by doubling the current it pulls, 166 tenths from a 150-tenth circuit the room believed : 1000 W, warm in twice the time actual : 500 W, warm in 4 times the time is the element damaged : no; it runs cool and happy is half the voltage half the heat : no; it is a quarter, and the transformer that fixes it trips the breaker null control - square the voltage power, read as half of rated : 1000 W power, read from voltage squared : 500 W watts the second halving removes : 500 no heater and no supply changed; the current was allowed to fall along with the voltage it depends on what a resistive heater on half its voltage guarantees it draws half the current : exactly, 41 tenths of an amp it gives half the heat : not addressed; heat is voltage times current and both halved, so 500 W, a quarter, and the transformer that restores 2000 W pulls 166 tenths through a 150-tenth breaker halve one thing that is really a product of two and you have halved it twice; the voltage you can read on the wall, the current you cannot, and the heat is the pair of them Half the voltage is half the current - that step is right. But the heat is their product, so 120 V into a 2000-W element is 500 W, a quarter, taking 4 times as long, and the transformer that gives the full 2000 back draws 166 tenths of an amp past a 150-tenth breaker, until the heat is read as the product it is. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done